INSTITUTE of STATISTICSOxford

IS THERE BIAS IN THE INTERIM INDEX OF RETAIL PRICES?

It is sometimes forgotten by those using the Interim Index of RetailPrices that the index strictly measures the increase since June 1947 ofbuying the average budget of the employed working-classes in 1937-8. Itis not an index which measures the increase in the working-class cost-of-living since 1947, in the sense of the increase in the cost of buying thebudget of the working-classes and those who constructed it did not havesuch an end in view. It, however, is often used for this purpose, such a usebeing implied for example in all comparisons between movements of thisindex and the new wage-rate index. This mistake is a natural one, seeingthat the Ministry of Labour uses June ¡947 as the base date for the index(because of the Ministry's unwillingness to publish its calculations of theincreased cost of buying the 1937-8 budget since ¡937-8).' This paperexamines whether and to what extent there is bias in the Interim Index whenit is used for this purpose.

Since there is no national survey of working-class expenditure in 1947available, we cannot answer the question directly. What we can do, however,is to apply the percentage distribution of weights in the new index to theestimated working-class expenditure in ¡947 and see what working-classexpenditure on each commodity group is implied. Then we can comparethe implied working-class spending with total national expenditure for eachgroup, as shown by the National Income White Paper, to estimate whatproportion of national expenditure is implied as working-class by the weight-ing system.2 These proportions can then be compared with the pre-war ratiosof working-class to total expenditure calculated from the 1937-8 budgetsand published in the BULLETIN for June 1948. Such a comparison wouldof course not reveal very small errors in the weights.3

Working-class income net of taxes in 1947 was estimated by the authorin the October 1948 BULLETIN as 4,735 millions. This estimate was ujltup as follows

See BULLETIN. May 1948, for a full account of this question. The fact that the wage.rate index, which does have a post-war weighting system, starts at the same base dateonly adds to the likelihood of misunderstanding.

l The use of percentages at June as annual averages will involve practically no error.The word' error' here means an error when the index is used for estimating current

changes in the working-class cost-of-living.

Bulletin Vol. 11 January, 1949 No. 1

Wages and direct taxes on wages are given in the National Income WhitePaper, and the estimate of the main item, net wages, is therefore a firm one.All but o millions of social security benefits were assumed paid to theworking-classes. So was half of H.M. Forces' pay and War Gratutities, andthe same proportion of salaries and property income as before the war. Theworking-classes were assumed to pay the same proportion of taxes on salariesand property income as pre-war. These assumptions make the total estimatetoo low, and were deliberately chosen in the original calculations so as not tooverstate the redistribution of income that was revealed in the paper. It isreasonable to suppose, for example, that 'working-class' salaries (thoseunder £250 in 1938) have increased in greater proportion than other salaries,and hence that the working-class share of the national salary bill will haverisen. This distortion may mean that the estimate shown was anything fromabout o millions to Laso millions too low, and we shall estimate working-class net income in 1947, for the purposes of this paper, as £4,900 ± £100millions.

It would seem from estimates made in the June 1948 BULLETIN thatworking-class savings were in 1938 about £170 millions, of which about £5omillions were increases in institutional funds, and other forms of impersonalsavings. Of total national savings in 1938 £'57 millions were personal and£i82 millions impersonal (including additions to tax reserves). In 1947national savings were £495 millions personal, and £210 millions impersonal, atotal of £705 nillions. In view of the restrictions on middle-class personalexpenditure and the substantial undistributed profits, working-class savingsmight be a lower proportion of both personal and impersonal savings thanpre-war. However, there is no way of estimating this directly so it will betaken as £200L400 millions, to allow a safe margin.

Working-class expenditure on consumption in 1947 was therefore :-

¿ millionNet Working-class income ... 4,900 ± looLess Working-class savings ... 300 ± 100

Working-class expenditure . . - 4.600 ±200

The table below shows the result of applying the weights of the InterimIndex to this estimated expenditure, the working-class share of expenditureon each commodity group that is implied, and the 1938 share' for the purposeof comparison:-

'BULLETIN, Vol. 10, p. 191.

2 THE BULLETIN

( millions)Net wages 3.261Net salaries 566Net pay of H.M. Forced 167Net property income ............ 234Social income 507

Net working-class income ... 4.735

Commodity Weight 1947 Working- 1947 Total Implied Working.Group in class expendi. national working- class share

Interim tore implied expendi- class share in expend-Index by index tore in expendi- iture in

weights tore in 1947 1938

Notes on the Covevage.I (National Income White Paper Group 1). National expenditure includes the food

element in meals out. These are apparently excluded from index weights, but spending onmcals out was actually spread over all groups to arrive at weighting, so that it is implicitlyincluded.

II (National Income White Paper Group 4). National expenditure includes an allowancefor buildings occupied by non-profit-making bodies, and for hotels, boarding houses, etc.,but excludes rents above Schedule A valuations.

III (National Income White Paper Group 8).IV (National Income White Paper Group 5). National expenditure, by contrast to the

Index, excludes candles.V (National Income White-Paper Group 6). National expenditure excludes wireless

sets, musical instruments, cycles and sports goods.VI (National Income White Paper Groups 7. 9 and 15). National expenditure includes

the goods mentioned in flotes on Groupe IV and V.VII (National Income White Paper Groups 10, 11, 12, 13 and 14). Index excludes

insurance and trade union services.VIII (National Income White Paper Groups 2 and 3).

(For 1938, the working-class share is calculated from estimates adjusted for thesediscrepancies.)

When judging the working-class share of consumption, it should be bornein mind that the working-class proportion of the population appropriateto the definition of 'working-class' used for income estimation has beenestimated at 84%. It should also be remembered that food, rent, and fuel andlight tend to be overstated in budgets, because budgets tend to be furnishedby the more careful people who might be expected to spend more on suchthings, and these items are also less likely to be forgotten than luxury spendingwhei. budgets are completed; and the proportions shown for 1938 should bejudged accordingly.

Let us examine in detail the last two columns of the Table, to see whatchanges in the working-class share of consumption are implied, and whetherthese changes seem plausible.

Rationing will have increased the working-class share of food consump-tion by 1947, and the Index weight may therefore be about right, providedit is understood that 'meals out' are meant to be included (otherwise itwould be slightly excessive). It is unlikely, however, that the working-class

'BULLETIN, Vol. 10, p. 187.

( million) ( million)I Food 348 1531-1670 1995 .77.84 .73

11 Rent 88 387-422 564 .69.75 .59III Clothing 97 427-466 704 .61.66 .46IV Fuel and Light 65 286-312 310 .92-1.01 .73V Household durables 71 312-341 393 .79-87 .50

VI Miscellaneous goods 35 154-168 560 .28.30 .37VII Services 79 348-379 1377 .25-28 .30

VIII Drink and Tobacco 217 955-1042 1368 .70-76 .60

Total ... 1000 4400-4800 7271 .6l-66 .55

IS THERE BIAS IN THE INTERIM INDEX OF RETAIL PRICES? 3

TABLE

4 THE BULLETIN

are paying a substantially higher proportion of the national rent bill, in viewof rent control and the housing immobility of the public, and it seems thatthe weight attached to rent is too high. The rise in the working-class shareof clothing since 1938 implied by the table is not impossible, in view of therestrictions exèrcised by rationing on middle-class clothing expenditure,and the possibility that the 1938 proportion was too low, and if there areerrors in the index weight for clothes, they cannot be large. The proportionimplied for fuel and light is clearly too high. Even though the estimate ofthe pre-war proportion is unreliable, the per capita working-class consump-tion is hardly above that of the middle-class, as is implied by the index weight,which is, therefore, too high. Similarly, the implied working-class expendi-ture on household durables appears excessive, even though the index weightincludes some items, not a great proportion of the whole group, excludedfrom national expenditure. The weight for Group V is, therefore, alsoconsidered too high.

On the other hand, though the apparent working-class share in 1947 isdepressed by the inclusion of some extra goods in national expenditure,Group VI, Miscellaneous Goods, seems to be substantially underestimated.There is no reason to suppose that the working-class share of these goods hasfallen. On the contrary it has probably risen considerably. The same appliesto Services, for which the Index weight is also apparently too low, althoughthe pre-war proportion includes trade union and insurance services whichraise it slightly. Still it is almost certain that the working-class share in 1947was above pre-war, in view of the increase in the working-class share of totalconsumption, and the known availability of working-class income for suchnon-essentials in 1947. Since the estimate of pre-war working-class con-sumption of drink and tobacco was taken from an (apparently) arbitaryMinistry of Labour estimate (shown in Supplement No. z to the IndustrialRelations Handbook), it is not of much use for comparison with the impliedworking-class share of 1947 consumption, and we can reach no conclusionon the extent of error for this group, except that it would not seem to belarge.

The conclusion one reaches therefore is that rent, fuel and householddurables are rather overweighted, while miscellaneous goods and servicesare probably underweighted, if the index is used for a comparison ofcost-of-living movements since June 1947.

Some check is provided by the working-class budgets for the summer of1947, collected by the Institute of Statistics.' If we take the 67 families of thesample which show their total post-tax income (since only in these cases isthere any check on non-household expenditure), and subtract insurancepremiums and club subscriptions, as being mainly saving and in any caseexcluded from the scope of the Index, we have the following weightingsystem implied, compared to the Index weights.

1T. Schulz, Family Expenditure in 1947, BULLETIN, Vol. 10, No. 11.

IS THERE BIAS IN THE INTERIM INDEX OF RETAIL PRICES? 5

Index Category Institute IndexBudgets Weights

I Food 366 348II Rent 86 88

III Clothing 76 97IV Fuelandlight .... 54 65

V_\TIII Miscellaneous 418 402

1000 1000

Since the families of the sample all had children, their budgets wouldtend to exceed the working-class average in the proportion of expendituredevoted to food. So this sample's results are not inconsistent with the beliefthat food is about correctly weighted. Rents in the sample budgets are biassedupwards because they exclude rural communities. Here, therefore, theprevious conclusion about over-weighting is confirmed. Since the budgetsrefer only to two summer weeks, some clothing purchases may have escapedthem, and large purchases out of savings are excluded during computation,so the actual proportion spent will be higher than shown by the budgets, andwe cannot draw any conclusions about the weight for clothing. It is unlikelythat fuel consumption of the working-classes is sufficiently affected by seasonalfactors to account for the difference in the weights shown above.' And theunderweighting on balance of Miscellaneous items (which include HouseholdDurables, believed to be overweighted, and Miscellaneous Goods andServices, believed to be underweighted) is also indicated. On the whole,however, there do not appear to be very drastic errors in the whole structureof weights.

The errors that are revealed accord with what one would expect.The index weights were constructed by correcting the 1937-8 weights forprice-changes, whereas what we want for this purpose are corrections forchanges in relative values of expenditure, i.e. for both prices and quantities.Where relative quantities purchased have fallen, i.e. where the real quantitybought of a group has not risen as much as total real consumption, because ofrationing or shortages or because income elasticities of demand are lowz(Housing, Fuel and Light, and Household Durables), the index weights aretoo high. Where there have been less limits on quantities bought or incomeelasticities of demand are high (Miscellaneous Goods and Services), theweights are too low for post-war comparisons. In the case of Food, Clothing,and Drink and Tobacco, working-class quantities purchased may not haveincreased in greater proportion than all working-class purchases, when theshortages in 1947 are remembered.

Whether the errors in the weights bias the Index depends mainly on thecorrelation between these errors and the price relative being weighted. Itcan easily be shown that if'I' is the true index number; 'I" is the biassedindex number; 'e' is the error in any relative weight, 'w'; and ' p' is theprice relative being weighted:

'In view of the tact that the summer sees building of domestic coal stocks'Strictly what concerns us here is the expenditure elasticity of demand,

6 THE BULLETINriw

Since we cannot estimate the crrors accurately, we cannot estimate rep.Its dimensions can, however, be indkated for the comparison June 1947-October 1948, by seeing whether high price relatives are associated withpositive or negative errors in the weights. Taking the first column from theNovember Ministry of Labour Gazette (arranging the items in the order ofprice relative) and the second from the conclusions above, we have

October 1948Commodity Group Price relative Sign of apparent

Uune 1947= 100) erro? in weightIII Clothing 114.1 nilIV Fuel and Light 112.0 +

VIII Drink and Tobacco 110.8 nilVI Miscellaneous Goods 109.3V Household Durables 108.5 +

All Ite,ns 108.4I Food 107.6 nil

Vn Services 105.1II Rent 99.5 +

It can be seen that the correlation between errors and price relatives islikely to be small. The order of positive and negative errors is about sym-metrical. If the errors in the weights were equal, the sign of r would be veryslightly negative. Of the items shown Clothing, Drink and Tobacco andFood can be ignored, as showing no or small errors. Household Durablescan also be ignored as showing virtually no deviation from the generalaverage, and so can Miscellaneous Goods because the deviation from theaverage price movement is inconsiderable and the weight attached is so smallthat errors in it are also likely to be small. The question is whether thenegative product between the error in the weight given to Rent and thedeviation from the unweighted mean of price relatives outweighs the positiveproducts in the case of Fuel and Light and Services. The net effect will besmall, and the dispersion of price relatives is in any case small, so it can betaken that the index shows practically no bias for this period. Possibly,however, the slow widening of choice provides possibilities of substitutionwhich amount to a slight upward bias in the index.

It does not necessarily follow, however, that the index is going to beunbiassed for any period. If we take the period June 1947 to January 1948,for example, the underweighted price relative for Miscellaneous Goods was 7points above the general average, and the overweighted item Rent was below.For this period the index therefore probably had a slight downward bias,understating the increased cost of living.

Bias will also appear, of course, if there is so much concern about move-ments in the index that price policy is administered to give relatively mostassistance to the overweighted items, achieving artificially a negative corre-lation between price relatives and errors in the weights. This was thetechnique used from 1941 to 1947, when the true cost-of-living, in the

Overweighted hemsMeat and baconsFatsCoal and cokeFurniture and furnishingsSoapMens clothing5

(Asterisks denote items where

IS THERE EIAS IN THE INTERIM INDEX OF RETAIL PRICES? 7

sense of the relative cost of buying what was bought pre-war, and the officialcost-of-living index diverged increasingly sharply.8 So successful was thispolicy that the official index eventually only showed half the rise that ought tohave been shown, thereby achieving a considerable restraint on wage increases.

The general structure of errors, with identifiable necessities overweightedand miscellaneous goods and services underweighted, provides possibilitiesof bias along the same lines as those previously employed. In order to shewthe possibilities of manipulation of the index that still exist (in case suchmanipulation seems desirable in the event of war or other economic disaster)the under- and overweighted commodities in the index at presentand theyare not likely to alter substantially so long as economic difficulties and ration-ing continueare listed below. They have been found by an extension tosubsections of the index of the techniques already used. Other commoditiesdo not appear to be seriously incorrectly weighted.

Undeweigh1ed flenasFishPotatoes and vegetablesElectricity5TravelEntertainments

the errors in weighting are substantial.)

Since the general economic position has not changed much since 1947,the errors in weighting involved in using June 1947 as a base will not be greatlydifferent from those involved in using a later date as a base, e.g. for month-to-month comparisons. Drink and tobacco may now be slightly overweighted,furniture may be less overweighted, and entertainments less underweighted,but the general structure of errors will be the same. On the whole one wouldexpect these errors to diminish if and as the working-class is able to approachmore nearly to its pre-war pattern of consumption,9 and consequently thepossibilities of manipulating the index may also tend to diminish. If economicequilibrium is restored, however, it will doubtless be found that some changesin the pattern of working-class consumption have become permanent, withcorresponding permanent errors in the index. It will then be desirable,of course, to change to a new Index with a post-war weighting system.

Apart from errors given to the weights in various subsections of theIndex, bias may be consciously or unconsciously introduced by gaps inthe items which are priced for the Index. In each section representativeitems only are priced. These representative items are listed in SupplementNo. 2 to the Industrial Relations Handbook.

The list of the items whose prices are taken into account when calculatingthe index omits for example the following commodities.

Special breads, veal, poultry, kidney, ham, shellfish, fish and chips, driedeggs, brown sugar, honey, pears, plums, nuts, invalid foods, animal foods,pepper, mustard, rice, sago, semolina, pies, chocolates, ice cream, coffee,

1 For a rough indication of this divergence, compare lines 1 and 4 of Table XVII inBULLEtIN, Vol. 9, p. 248.

We are concerned here with the physical pattern, not the expenditure pattern.

8 THE BULLETIN

pickles, canned peas, soups, furnished lodgings, pyjamas, belts, scarves, ties,handkerchieves, men's gloves, aprons, brassieres, nightgowns, dressing-gowns, nylon stockings, infants' vests arid pants, cotton clothing materials,men's slippers, men's wellingtons, football boots, anthracite, firewood, fire-lighters, chairs, pianos, kitchen tables, garden furniture, desks, fenders,pillows, cushions, lamp shades, pipe and cigarette lighters, gas mantles,watches and other jewellery, gramophones, toys and games, footballs, carpetsweepers, coconut matting, doormats, tablecloths, pillow cases, quilts, faceflannels, dustpans, shovels, hammers, screwdrivers, saws, axes, fireguards,clothes' horses, pokers, tongs, mops, dusters, dishcloths, bread bins, cookingtins, frying pans, colanders, tin openers, pastry boards, bread boards, hairbrushes, saucers, jugs, cleansing fluids, shampoos, shaving soap, steel wool,disinfectant, toilet rolls, toothbrushes, powder puffs, shaving brushes,contraceptives, darning wool, needles, pins, sewing cotton, pens, ink, pencils,rubbers, string, envelopes, coach fares, shipping and ferry fares, motorcycles (and cars), telephone calls, telegrams, admission to theatres, dances,boxing matches and greyhound meetings, use of billiard saloons, foot-ball pools, bookmakers' services, restaurant and boarding house services,undertaking, insurance services, legal services, technical training and educa-tion, stamp duties, hire of heating apparatus, gin, rum, wines, snuff, cigarettepapers, tobacco for cigarettes.

Changes in the prices of any of these will not affect the Index at all. It isnot suggested that such omissions are in any way improper or that these itemsare appropriate for pricing. In fact the items chosen as representative seemreally to be so, so that in normal times these gaps will not matter. This listdoes indicate, however, the extent of the deficiency in coverage and hence thepossibility of manipulation provided by the Index, as indeed by all priceindices. In addition further possibilities lie in the fact that usually, accordingto the Supplement, the price relatives for selected items of each subsectionare combined in an unweighted average, although, of course, the weightsappropriate to different price relatives may be very different.

Broadly speaking the position at present is that the reduction of foodsubsidies or increased coal prices would cause disproportionately large move-ments in the Index, as would the relaxation of rent control, whereas fareincreases, extra amusement taxes, dearer electricity or increases in the wages ofthose in service industries (particularly catering) are measures which wouldnot affect the Index proportionately to their effect on the actual cost ofliving. The effect of reduced purchase tax would depend entirely in the itemsselected for reduction.

While, therefore, the Index is not intended to measure changes in theworking-class cost-of-living the widespread habit of using it as a post-warcost-of-living index has not in practice been seriously erroneous so far.Inappropriate weights and gaps in the Index, however, may make such a usepractically as well as theoretically incorrect in the future, particularly if sucherrors and gaps are used deliberately to bias the Index.

DUDLEY SEERS.